A Diffusion-Based Approach to Missing Data in Binary Time Series

We consider the application to a real dataset of previous results on Wright–Fisher hidden Markov model smoothing in the non- informative prior specification. Specifically, we consider a financial binary time series with missing data and exploit the smoothing framework to infer the latent signal at time points where observations are unavailable. To validate the approach, we perform inference at time points with both observed and unobserved data, thereby obtaining a direct assessment of calibration. For each time point we report posterior uncertainty through credible intervals, which consistently cover the empirical proportions on observed days. This provides evidence of good finite-sample performance and supports the reliability of the resulting estimates at missing times.